FPGA-Based 8x8 Bits Signed Multipliers Using LUTs
Bibliographic record
Abstract
Modern FPGAs (Field Programmable Gate Arrays) like Xilinx 7-series ones incorporate DSP blocks that contain 18x25 bits two’s complement embedded multipliers. When FPGA-based small size signed multipliers are required, it is not practical to use these large size embedded multipliers. Thus, one can use LUTs (Look Up Tables) in FPGAs to implement them. Since the target signed multipliers are assumed in two’s complement, a preprocessing is required for a LUT-based implementation. In this paper, Baugh-Wooley and sign-magnitude are used as preprocessing algorithms to realize two’s complement 8x8 bits multipliers using LUTs in FPGAs. These two algorithms are used since they allow for a parallel realization of the signed multipliers. We synthesize 8x8 bits two’s complements multipliers on LUTs using these two algorithms. As an application, we use the resulting synthesized designs to synthesize 8-taps and 16-taps digital Finite Impulse Response (FIR) filters for input data and coefficients in two’s complement. Experimental results on Xilinx Artix-7 FPGAs using the Vivado 2020.2 synthesis tool show that the synthesized designs using the Baugh-Wooley algorithm are better in terms of speed and area compared to using the sign-magnitude.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".